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Game theory has been used to explore different scenarios where different forces interact. In economic theory these forces can be market forces but the interactions can also be between sets of people. One early example is Nash Jr (1950), where a game with a finite set of actions must have an optimal strategy (the Nash equilibrium) for actions if the other players’ set of actions are known and are not dynamic. Agent simulation has been used to model interactions between individuals to solve game theory scenarios such as the prisoner’s dilemma scenario, a game to study whether you should cooperate or defect against your comrade. If you both defect you both lose, if you cooperate you both

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win, but if one defects and the other cooperates the defector wins. Here Axelrod and Dion (1988) simulated an iterative version of the prisoner’s dilemma and found that the optimal simulation model configurations were the ones that employed a tit-for-tat strategy. Axelrod later went on to test this with agents using a genetic algorithm (Axelrod,1997); finding that 95% of all populations evolved towards the optimal tit-for-tat strategy. The problem with the optimal tit-for-tat is that the decisions do not incorporate fairness into the decision making process. In response, Rabin et al. (1993) created a framework to include fairness into game theory decision making, where a player’s payoff would be derived not just from their actions but also from their beliefs about the situation. For example, if a player thought that their opponent was going to defect they would be willing to sacrifice their reward to hurt the other player.

Computers have been used to simulate group decision making since the 1960’s. Abelson and Bernstein (1963) worked on the computer simulation of a community referendum. They were able to run a number of different configurations of their simulation model to study differing assumptions and conditions. Computerised individuals were subject to channels (advertisements) and conversations which would influence the way in which they would vote. The individuals could influence others in their proximity based on their idealogical understanding. This understanding was based on what they had learnt during the previous cycle. The level an individual could be influenced was dependent on a set of predefined rules. Abelson and Bernstein (1963) ran scenarios to examine their effect on the results, ie. what if a mayor was introduced with more influence towards one side, what would happen if this mayor did something controversial, etc.

Researchers in the field of agent based social simulation have used a cognitive theory to model people, a classic example is the unified theories of cognition. Newell (1994) devel- oped unified theories of cognition into an example framework, describing the immediate process of cognition and learning. This has been used as a method to create the Soar agent system (Wray and Jones,2006), within which there are three levels; the knowledge level (a descriptive view of the agent’s understanding), the symbol level (the representation of that knowledge), and finally the architecture (the fixed mechanisms that define the ways in which knowledge is accessed and acted on). The Soar agent system has been extended to include interactions between agents through STEAM (Tambe,1997). STEAM uses the understanding of joint intentions (Cohen and Levesque, 1991) where agents who have a joint understanding of their current state and a shared goal can perform an action as a group; either one agent performs it or they perform sequential actions to achieve the goal. This model must adhere to the following requirements: the agents must have a joint goal, must be willing to co-operate, to agree on how to achieve the goal, and the agents must understand the viability of their actions (Jennings,1995). The joint intentions approach

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has a weakness though. When an agent commits to a common goal, what happens when something goes wrong? Do all the agents continue on the same agreed path, even though the goal will not be achieved? What happens if one agent believes the goal has been met or will never be met? In an attempt to resolve thisJennings(1995) built into the model a concept of joint responsibility, requiring all agents to share why they have a lack of com- mitment to the persistent goal. This allows the other agents to assess the situation and decide on remedial actions. Related to the joint intentions method of collaboration is the SharedPlan approach (Grosz and Kraus, 1996). Agents using the shared plan have their own beliefs, intentions and goals. Any intentions that may affect other agents need to be communicated, and these intentions are then meshed into plans of action. This method allows for agents having partial information about another agent’s understanding, but they must have sufficient information to allow consensus. Within the SharedPlan formalisation agents cannot hold intentions that conflict with each other.

The joint responsibility and shared plan methods assume there are common goals between agents or common actions that can be achieved. However, this is not always the case. There are times when an agents’ goals are in direct conflict with those of another. In this case mediation is required to allow them to move towards an optimal solution for both parties. The PERSUADER program is a system that focuses on resolving labour disputes (Sycara, 1988). It works through proposals and modification of goals. Goal trade-offs are searched allowing the PERSUADER to make novel proposals. Agents continually re-assess their beliefs, so that what may not have been acceptable at one point may be acceptable later. An initial plan is made, and evaluated against previous plans. If it is acceptable it is proposed to the agents, who either agree or disagree. Disagreement allows for discussion between agents, then either modification of the plan or the process starts again with a new plan created. The argument stage works by changing the agents’ belief structure. For example, with a wage dispute a company may request a lower wage for the union, this is against their goals, PERSUADER checks the possible alternatives, finding that unemployment will achieve the same goal for the company. This approach is worse for the union and the PERSUADER program highlights this to the union allowing them to reassess.

Over time the goals of an agent may change. Kraus et al.(1995) builds a time restraint into the decision making process, where resources are valuable when there is a disagreement and each agent has a period of time before the resource is no longer useful. The time constraints alter the decision being reached and can often determine the agreement. For example, if two agents want access to a resource within a period of time, they can negotiate an agreement based on the value of the resource and the cost of deliberation. Davis and Smith (1983) developed a method of negotiation to resolve distributed problem solving.

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Called the contract net, agents bid for tasks agreeing that they will complete one for a given price and if a contract is agreed for the winner. The framework then distributes the tasks to the winner of the contract. This has been developed into a multi-agent system called TRACONET, which allows agents to announce bids for an available task, the lowest bid over a period of time requires that an agent is committed to completing the task (Sandholm, 1993). An agent calculates their bid based on a local calculation of the cost of performing the task; they combine multiple tasks to minimise their costs. The TRACONET system was developed for transportation agents, with the example of delivery companies. The cost of the task would be the time to make a delivery and the deliveries are chained to ensure they end near the start of the next delivery. TRACONET was further developed allowing agents to assign different levels of commitment to each task (Sandholm and Lesser,1995); now agents can back out of a task for a cost if they see that another agent is committed to the task and they believe that they can get a better deal elsewhere.

Agents that can learn another’s preferences have been demonstrated to find an optimal solution to conflict resolutions. In the example of a Bazaar, agents negotiated prices for products, moving towards a price they would sell or buy at (Zeng and Sycara, 1997). Both agents have conflicting goals but, if they had a price point that was acceptable to them both, they could eventually agree. If the buyer and seller could learn the other’s preferences they came to an agreed price quicker than one that could not learn the other’s preferences. Shoham and Tennenholtz (1992) presents a method of conflict resolution called social laws; constraints that should be built into the actions of the agent. They avoid conflicts and the unnecessary negotiations by removing conflicts from the system before a simulation takes place. An agent has a choice of actions that can be performed at a given state, but before taking an action the agent must consider a set of social laws. These define which actions the agent can take to ensure that no conflicts occur. The example used byShoham and Tennenholtz (1992) is of a car turning a corner, the car can only turn if the driver understands the lights are green and no other car is in the location that the car will occupy once around the corner. This approach assumes all agents have the same set of social rules.

The modelling of multi-agent group decisions is either centralised or decentralised. In the centralised model an agent has a complete understanding of the environment and a decision is made to maximise global utility, ie. to keep everyone happy. In the decentralised model each agent communicates, gains an understanding of the environment from their perspective and makes a decision to maximise their local utility. One method of forcing decentralised communication is by adding cost to any communication taking place. To model a multi agent decision process between distributed systems Xuan et al. (2001)

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developed a decision theoretic framework. This relied on each agent having the same goal to maximise the global utility. Each agent would have an incomplete understanding of the environment, the agents would only communicate up to the point where the reward would outweigh the cost of communication. This means that an agent’s beliefs about what action to take to maximise utility can be changed through the communication process.

The Clarke Tax (Clarke,1971) has been used to allow agents to come to a consensus and remove the free rider problem, where an agent may lie about the benefit of a resource to gain more at a discount. In Ephrati et al’s1991system agents declare their preference for reaching a state from amongst a set of states. If their preferences are the deciding factor between the voters they are taxed the difference between the sum of preference of the first and second choice of states. This forces an agent into telling the truth of the true value of their vote. If they do not and they win through a higher vote they will be taxed higher for their choice. This method has its drawbacks, it does not consider how the resources are divided between the winning agents of the vote; on the other hand the voting strategy is a quick and effective method of arriving at a consensus.

As outlined many of the methods that are used to allow agents to reach a goal, either in cooperation or in conflict. Within No-MASS a simplified variation of the the voting mechanism to overcome conflict (Ephrati et al.,1991) is proposed. Then once the agents are in agreement over which action to take, No-MASS use’s social laws (Shoham and Tennenholtz,1992) to decide how the action will take place. For example, agents will vote on whether they want to open the blind and once votes are cast, they decide how far the blinds will be opened.

6.2

Implementation

Social interactions are an important consideration when modelling occupants. Decisions such as opening windows and interacting with shading devices are often discussed between occupants before an interaction is performed. The current convention of building perfor- mance simulation tools is to assume that all occupants within a building interact with the environment at a given set point of a particular variable, i.e. indoor temperature for windows and internal illuminance for shades. Therefore, there is no need for a conflict resolution mechanism. But in reality occupants have different beliefs and desires about how they wish the environment to be. Group interactions with the environment are often achieved through group mediation, with occupants voicing their concerns about their dis- comfort. No-MASS agents are self interested. They act based on their beliefs about their current state of discomfort. Given a set of decisions each agent decides if they would like

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to open or close the window to minimise their discomfort. An agent does not consider the state of the other agents at this point, if they intend to open a window they must negoti- ate with the group. But one agent’s intent maybe in direct conflict with an other agent’s goals and desires. A notable solution to conflict resolution would be a voting system such as the one employed by Ephrati et al. (1991), which has be demonstrated to be a quick and effective method for arriving at a consensus. However, as No-MASS agents behave rationally based on the outputs of the stochastic models our agents do not suffer from the free rider problem, Ephrati’s system incorporates a tax system on choice to overcome this.

Occupants may have differing authority to make choices about the environment. Within No-MASS constraints can be placed on the actions that can be performed during a conflict; this is achieved through a biased voting system. Some agents can have larger voting rights than others, these voting rights are called power within No-MASS, these are social laws built directly into the actions. To demonstrate the mechanism three classes of group interaction have been chosen; these mimic possible scenarios in the real world; democratic, biased and authoritarian. Each will be explained and with a demonstration given of how they can be handled with this voting system.

Agent Agent 1 Agent 2 Agent 3 Agent 4

Democratic 0.25 0.25 0.25 0.25

Biased 0.18 0.18 0.18 0.46

Authoritarian 0 0 0 1

Table 6.1: Agent Voting Power

Our agents and voting weights are given in Table 6.1 for scenarios with a four member group. The first scenario is the democratic environment in which each agent has equal voting power for the interactions that they wish to perform. If a single agent wishes to open a window and another two are present in the zone then the other two can choose to either side with this agent given their personal preferences, or they can veto the window opening. In this case there will need to be at least two agent suggesting the window stays closed to win the vote. In cases where the agents votes are tied a virtual coin toss is performed to decide the outcome. A random number is drawn, if it is above 0.5 then one action is performed, if not then the other choice is performed.

In the second scenario, the biased approach, one agent will have the majority of the voting power as may be found in hierarchical organisations where a group goes along with a supervisor’s preferences. In most cases the supervisor’s vote will win, however if the other agents disagree they can pool their voting resources together to veto the action.

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Finally there is the authoritarian scenario where if present one agent has all the power, the others can perform actions when the leader is not present, but they do not have the ability to override the agent.

This approach works well in binary cases where the actions are on/ off, such as for the lighting model. However models such as the external shading interaction model predict a shade opening fraction. An agent has a choice of actions that they can take to either raise, lower or keep the shades as they are. Given a set of agents, one could choose to raise the shade to a percentage and the other lower the shade. In the first instance the voting mechanism can be used; agents can vote to raise, lower or do nothing to the shading device. To determine the percentage change that occurs, social laws (Shoham and Tennenholtz,1992) are enforced on the agent, removing the need for time consuming negotiation. A set of two agents choose to raise the shade from its current position but they both choose to open it to different levels. Here a restriction is imposed on the agents that they must choose the average of the two. This will satisfy the agents’ need to raise the blind and allows the simulation to move on (however it may please neither agent). Within No-MASS agents assess their personal preferences at each timestep for all the stochastic models, the agents will therefore have to resolve conflicts at each timestep. This methodology of processing votes does not increase simulation time significantly and provides a first instance of agent negotiation within buildings; the effects of which will be discussed later in this chapter.